Scottish ministers are being urged to reverse cuts in student grants after the debts taken out by Scottish students to meet their living costs soared by £160m last year.

New analysis of the latest figures from the Student Loan Company shows that overall student debt rose far more sharply in Scotland than anywhere else in the UK in 2013-14. It jumped by a record 58% to £436m for the year.

Lucy Hunter Blackburn, a former Scottish government civil servant who helped devise the graduate endowment levy on post-university earnings that was scrapped by Alex Salmond in 2007, said her analysis showed this was the highest annual rise in total student debt in any part of the UK since the mid-1990s.

Loans taken out to cover daily living costs, the category over which Scottish ministers have direct control, jumped by 64% to £409m after the government in Edinburgh slashed maintenance grants to fund other policies in 2012.

Hunter Blackburn said her analysis showed that while Scottish students had the lowest average debt in the UK, at £5,344 per head against £8,924 in England, £6,191 in Wales and £6,214 in Northern Ireland, most did four year degrees. That implied their total debts at graduation would be more than £20,000.

Announcing the new funding scheme in 2012, Mike Russell, Scotland's education secretary, played down the greater use of loans by arguing the new package would give Scottish students the most generous deal in the UK, entitling them to a minimum of £7,250 overall.

The National Union of Students said it wanted ministers to increase student grant funding significantly in next year's budget, without reducing the loans available to those who needed them and without changing the free tuition fees policy, which it heartily supports.

Gordon Maloney, the president of NUS Scotland, said: "We will be working with the Scottish parliament to push for increased grants for the poorest students, not instead of these student loan increases, but in addition."

Scottish Labour said the surge in debts raised serious questions about the government's overall funding of education. The Scottish National party won power in 2007 in part by pledging to abolish all student debt, but had since slashed college funding and then cut grants, putting greater pressure on poor students.

Neil Bibby, Scottish Labour's deputy education spokesman, said: "The SNP has already reduced grants which means many Scots from poorer backgrounds are less able to access university education.

"The drastic rise in student loans being taken out it is clear that the SNP need to think again about how to support students and they could start that by reversing the cuts to bursaries for the poorest students."

Hunter Blackburn said overall Scottish debt levels would increase further once extra loans taken out during the full academic year following the 2012 reforms were counted. Student Loan Council data was for the financial year, and the full academic year figures are due out in October, after the Scottish independence referendum.

Hunter Blackburn said that by comparison, student debt rates in England, where loans also cover tuition fees of up to £9,000 a year, increased by 26%. In Wales and Northern Ireland, which have more generous student support policies, the rises were 15% and 8% respectively.

Student debt rates have been rising consistently faster in Scotland since 2011, increasing by 85%, compared with 51% in England over those two years.

The Scottish government did not dispute Hunter Blackburn's analysis, but said it was clear that Scottish students still had lower debts on average than others in the UK. A spokesman said the loans offered students more flexibility in how they supported themselves. In addition, 12,175 college students received educational maintenance allowances worth £8.3m in 2011-12.